(1)Faulty throughout bearing
(2)Faulty pilot bearing

Let's examine each of these possibilities. While releasing the clutch pedal, the clutch linkage pulls something called a throughout bearing away from the pressure plate. The pressure plate is then able to press against the clutch disc causing the clutch to become engaged. Now, as the throughout bearing is being pulled away from the pressure plate, it is rotating. If it's faulty, it will often make some sort of noise (commonly that of a squealing/howling sound - as indicated in the problem.

In the second case, again, while releasing the clutch pedal, the clutch is engaging. This means something called the pilot bearing (connects the crankshaft to the transmission input shaft) will have stress on it. If it's faulty, it will similarly make a squealing/howling noise. By the way, if the noise is louder when driving up a hill as opposed to a flat road, it's more likely the pilot bearing is at fault.

What to do?

Unfortunately, there is no easy way around this problem other than having the clutch/transmission assembly opened up and examined by a mechanic. Hopefully, your car is covered under either some sort of warranty or a service contract. If not, try to find a car repair shop which is very reputable.